Rolling 100 dice and landing the same number
What has a 1 in a million chance? (2010)
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Re: What has a 1 in a million chance? (2010)
#82Picking an integer between 1 and 1000000 without replacement.
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Re: What has a 1 in a million chance? (2010)
#83Earlier quoted context omitted.
To save some time for the rest of us: > If we guess a President will serve on average about 6 years, then [1 in (6 times 4.0 million =) 24 million] babies will someday be President.
I prefer the interpretation of an ominous prediction that the presidency will be filled by 24 million babies someday soon. Switzerland does have a committee of 7 people as president, only a small step from that to 24 million babies.
Of course it's a very small step to make babies amounting to 3 times the current population of Switzerland (so assuming roughly a 50/50 female/male divide, everyone needs to make 6 babies on average, in the same year so they will still all be babies when the last one is born? that's probably impossible for the females but we are already way into the science-fiction category) and put them all in a committee.
The more I think about this, the funnier and more complicated this gets.
Re: What has a 1 in a million chance? (2010)
#84Rolling 100 dice and landing the same number
More like 8 or 9 dice landing on the same number.
Re: What has a 1 in a million chance? (2010)
#85Reminds me of https://markxu.com/strong-evidence «One time, someone asked me what my name was. I said, “Mark Xu.” Afterward, they probably believed my name was “Mark Xu.” I’m guessing they would have happily accepted a bet at 20:1 odds that my driver’s license would say “Mark Xu” on it. The prior odds that someone’s name is “Mark Xu” are generously 1:1,000,000. Posterior odds of 20:1 implies that the odds ratio of me…
This article seems to twist the definition of “extraordinary” to something clearly not intended by the original quote about claims and evidence. Mark is a very common first name. Xu is a Chinese surname shared by over ten million people (according to Wikipedia). It’s entirely ordinary that someone would have this combination of names.
Don't ask me why, but I had to urge to look up the number of Chinese surnames: About 2000 are currently in use, half the Han Chinese population uses just 19 surnames.
Quite low compared to the 850 THOUSAND (another source has more than a million) surnames used in Germany, twice as much as in Spain bespite it have a tradition of double-names. I guess Germany being such a central state with many migration waves over the last 600~800 years since family names have become common.
Re: What has a 1 in a million chance? (2010)
#86Reminds me of https://markxu.com/strong-evidence «One time, someone asked me what my name was. I said, “Mark Xu.” Afterward, they probably believed my name was “Mark Xu.” I’m guessing they would have happily accepted a bet at 20:1 odds that my driver’s license would say “Mark Xu” on it. The prior odds that someone’s name is “Mark Xu” are generously 1:1,000,000. Posterior odds of 20:1 implies that the odds ratio of me…
This article seems to twist the definition of “extraordinary” to something clearly not intended by the original quote about claims and evidence. Mark is a very common first name. Xu is a Chinese surname shared by over ten million people (according to Wikipedia). It’s entirely ordinary that someone would have this combination of names.
Someone, yes. The person in front of you? Unlikely.
Analogy: someone has a winning lottery ticket. Is it the one in your hand? Probably not.
Re: What has a 1 in a million chance? (2010)
#87Existing is such an unlikely chance that it's more likely we don't.
Re: What has a 1 in a million chance? (2010)
#88Earlier quoted context omitted.
This article seems to twist the definition of “extraordinary” to something clearly not intended by the original quote about claims and evidence. Mark is a very common first name. Xu is a Chinese surname shared by over ten million people (according to Wikipedia). It’s entirely ordinary that someone would have this combination of names.
Don't ask me why, but I had to urge to look up the number of Chinese surnames: About 2000 are currently in use, half the Han Chinese population uses just 19 surnames. Quite low compared to the 850 THOUSAND (another source has more than a million) surnames used in Germany, twice as much as in Spain bespite it have a tradition of double-names. I guess Germany being such a central state with many migration waves over th…
It's even more concentrated in Vietnam. A very large chunk of the country is called Nguyen. Korea has similar with Kim/Park/Lee.
Re: What has a 1 in a million chance? (2010)
#89Reminds me of https://markxu.com/strong-evidence «One time, someone asked me what my name was. I said, “Mark Xu.” Afterward, they probably believed my name was “Mark Xu.” I’m guessing they would have happily accepted a bet at 20:1 odds that my driver’s license would say “Mark Xu” on it. The prior odds that someone’s name is “Mark Xu” are generously 1:1,000,000. Posterior odds of 20:1 implies that the odds ratio of me…
Why is the 20 multiplied by the million? Why not 0.95 multiplied by million? Using the same argument I would accept infinite odds that my username is quickthrower2 so there is infinite information?
It's important to understand that when they said "bits" they didn't mean information in the Shannon entropy sense, but rather in the log-odds evidence sense.
Gaining a Shannon entropy bit means learning the answer to a yes-no question that had 1:1 odds.
Gaining a log-odds evidence bit means doubling your best-guess odds on a question you are uncertain about, from X:Y to (2X):Y.
One Shannon bit is worth arbitrarily many evidence bits, because a Shannon bit takes you from 1:1 odds to UNBOUNDEDLYHUGE:1 odds. So... yeah, actually, reading your username is worth infinite bits of log-odds evidence on what your username is! (Ignoring practical issues like the small chance of computer malfunctions, of course.)
And to answer your initial question: the 20 just came from the assertion they'd bet 20:1. That was arbitrary.
Re: What has a 1 in a million chance? (2010)
#90Rolling 100 dice and landing the same number
Yeah, no. Read the article. There’s an example with a coin flip, which only has two possible values, and therefore a much, much higher possibility than a dice.